Home > Problem of the Week > Archive List > Detail

 << Prev 4/6/2014 Next >>

## The Old New Math Revisted

Consider these test items from a SAT exam prior to 1965. The intent at that time was to start reflecting the "New Math" curriculum developed in the early 1960s.

NOTE: No slide rules (or calculators?) allowed.

[Q1] If there are 400 students in a school, which of the following statements is (are) true?
I. There must be at least one month in which 30 or more students have a birthday anniversary.
II. Some students must have birthday anniversaries on the same day.
III. Some students must have been born in the same year and on the same day.
(A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III

[Q2] Two variables in a scientific experiment are such that their product is always 1. If, for a certain time, one variable is greater than zero, less than 1, and decreasing, then which of the following best describes the second variable?
(A) Greater than 1 and increasing
(B) Greater than 1 and increasing
(C) Not changing
(D) Less than 1 and increasing
(E) Less than 1 and decreasing

[Q3] If x, y, z, and w are all real numbers and none of them is zero, which of the following expressions can equal zero?
I. x + y + z + w
II. x2 + y2 + z2 + w2
III. x3 + y3 + z3 + w3
IV. x4 + y4 + z4 + w4
(A) I only (B) III only (C) II and IV only (D) I and III only (E) I, II, III, and IV

[Q4] If x(x-y) = o and if y does not equal zero, which of the following is true?
(A) x = 0 (B) Either x = 0 or x = y (C) x = y (D) x2 = y (E) Both x = 0 and x - y = 0

[Q5] Of three coins, Q, R, and S, two are counterfeit. One counterfeit weighs more than the good coin, while the other weighs less. Q proves to be heavier than R when weighed. Which of the following statements is false?
(A) Q and S are counterfeit
(B) R and S are counterfeit
(C) Q and R are counterfeit
(D) Q or R but not both are counterfeit
(E) Q and R or both are counterfeit

[Q6] If # is an operation on the positive numbers, fow which of the following definitions of # is x#y = y#x?
(A) x#y = x/y
(B) x#y = x - y
(C) x#y = x(x + y)
(D) x#y = (xy)/(x+y)
(E) x#y = x2 + xy2 + y4

[Q7] Which of the following properties is (are) applicable to both the set of integers and the set of rational numbers?
I. Between any two of the set there is a third
II. There is a least positive number of the set
III. There is a greatest number of the set
(A) None (B) I only (C) II only (D) III only (E) II and III only

[Q8] How many numbers in the set {-5, -3, 0, 3} satisfy both of the conditions |n - 3| ≤ 6 and |n + 2| < 5?
(A) None (B) One (C) Two (D) Three (E) Four

[Q9] The number of points in the intersection of the graph of x = y and the graph of |x| + |y| = 1 is
(A) None (B) One (C) Two (D) Three (E) Four

Source: E. Rosenthal. Understanding the New Mathematics, 1965, pp. 17-19

Hint: This is a test...not hints available!

Solution Commentary: The listed answers are 1(B), 2(A), 3(D), 4(B), 5(E), 6(D), 7(A), 8(C), 9(C).

Do you agree?

And, do you feel that math has changed much in the last 50 years, based on these questions?